CA-CFAR detector detection probability analysis method and system under noise background

Abstract

The invention provides a CA-CFAR detector detection probability analysis method and system under a noise background, and belongs to the field of detection probability calculation methods. The objective of the invention is to solve the problem that there is no accurate analytical relationship between the detection probability and the detection threshold of the existing CA-CFAR detector. The method comprises the following steps: fitting probability distribution containing echo signal test statistics by using Gamma distribution, calculating signal amplitude, and calculating detection probability. According to the method, a calculation model of the detection probability is established, and the detection probability of the CA-CFAR detector under the exponential distribution noise background can be directly calculated; the problems that a traditional Monte Carlo simulation method is large in calculation amount and long in consumed time are solved, the calculation efficiency is remarkably improved, and a theoretical basis is provided for evaluation of the detection probability.

Description

Technical Field

[0001] This invention relates to the field of detection probability calculation methods, and more specifically, to a method and system for analyzing the detection probability of a CA-CFAR detector under noisy conditions. Background Technology

[0002] In active sonar detection, noise, as a major background interference, severely affects the detection performance of target echo signals. Therefore, researching detection techniques that can effectively detect echo signals in noisy environments has become one of the core issues in the field of sonar signal processing. Cell-Averaging Constant False Alarm Rate (CA-CFAR) detectors are among the most commonly used detector structures in active sonar due to their simple structure and ease of implementation. Currently, under exponentially distributed noise backgrounds, there is a lack of accurate analytical relationship between the detection probability and the detection threshold of CA-CFAR detectors. In engineering practice, the computationally intensive Monte Carlo simulation method is often relied upon to analyze the detector's detection probability; however, this method is inefficient and lacks theoretical support.

[0003] To address this problem, this invention proposes a novel solution: the probability density function containing the target echo detection statistic is fitted using the Gamma distribution, and an analytical expression for the detection probability is established. Summary of the Invention

[0004] The technical problem to be solved by this invention is:

[0005] To address the lack of an accurate analytical relationship between the detection probability and detection threshold in existing CA-CFAR detectors.

[0006] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0007] This invention provides a method for analyzing the detection probability of a CA-CFAR detector under noisy conditions, comprising the following steps:

[0008] S100. Fit the probability distribution of the detection statistic under the condition of target presence using the Gamma distribution, including calculating the real and imaginary probability density functions of the signal plus noise in the unit under test under the condition of target presence, then calculating the mean and variance of the detection statistic under the condition of target presence, and then calculating the shape parameter and scale parameter of the Gamma distribution under the mean and variance to obtain the probability density function of the detection statistic under the condition of target presence.

[0009] S200. Given the signal-to-noise ratio, reference cell length, probability density function of noise power level estimation, probability density function of detection statistic under target presence condition, and standardization factor, the detection probability is calculated.

[0010] Furthermore, in step S100, the detection statistic under the condition that the target exists... probability density function Shape parameters of the Gamma distribution Scale parameters of the Gamma distribution The expression is as follows:

[0011] (1)

[0012] (2)

[0013] (3)

[0014] In the formula, ; It is the Gamma function; For without coefficient and The product of the two, with coefficients set to ; The ratio of the instantaneous echo power to the average noise power in the unit under test is given by the relationship between the signal-to-noise ratio (SNR) and the signal-to-noise ratio (SNR). ;

[0015] Further, in step S200, the detection probability is... The expression is as follows:

[0016] (4)

[0017] In the formula, It is a generalized hypergeometric function. , , , It is the independent variable of the function. for exist Take 2, A special case when taking 1, Also known as hypergeometric functions.

[0018] A detection probability analysis system for a CA-CFAR detector under noisy conditions is provided. The system has program modules corresponding to the above steps and executes the steps in the above-described method for detecting probability of a CA-CFAR detector under noisy conditions when running.

[0019] A computer-readable storage medium storing a computer program configured to, when invoked by a processor, implement the steps of a method for probabilistic analysis of a CA-CFAR detector in a noisy environment.

[0020] Compared with the prior art, the beneficial effects of the present invention are:

[0021] This invention establishes a computational model for detection probability, enabling direct calculation of the detection probability of a CA-CFAR detector under noisy conditions. In existing technologies, there is a lack of analytical models that can directly and accurately calculate the detection probability of a CA-CFAR detector under exponentially distributed noise conditions. Currently, statistical calculations of detection probability typically rely on numerical simulations based on the Monte Carlo method, requiring numerous independent and repeated experiments and consuming significant computational resources. This results in a computationally intensive and time-consuming detection probability analysis in engineering applications.

[0022] This invention successfully establishes an analytical calculation model for the detection probability of a CA-CFAR detector under noisy conditions through rigorous mathematical derivation. Using this model, the calculation of the detection probability no longer relies on time-consuming Monte Carlo simulations, but is achieved through a near-instantaneous analytical solution process. This model significantly improves computational efficiency, greatly reduces the computational load and time consumption of detection probability analysis, thereby enhancing computational efficiency and practicality in engineering applications. Attached Figure Description

[0023] Figure 1 This is a flowchart of a method for analyzing the detection probability of a CA-CFAR detector under noisy background, as described in an embodiment of the present invention.

[0024] Figure 2 The above are comparison diagrams of the probability density function distribution of the detection statistic under the condition of target presence in the embodiments of the present invention. Among them, (a) is the statistical calculation result of the detection statistic under the condition of target presence when the signal-to-noise ratio (SNR) is -10dB and the probability distribution diagram of the Gamma distribution fitted by the present invention. (b) is the statistical calculation result of the detection statistic under the condition of target presence when the signal-to-noise ratio (SNR) is 10dB and the probability distribution diagram of the Gamma distribution fitted by the present invention.

[0025] Figure 3 The following are pseudo-color images showing the changes in detection probability with standardization factor and signal-to-noise ratio in embodiments of the present invention: (a) is a pseudo-color image showing the changes in detection probability with standardization factor and signal-to-noise ratio fitted by the Gamma distribution of the present invention; and (b) is a pseudo-color image showing the changes in detection probability with standardization factor and signal-to-noise ratio calculated by statistics.

[0026] Figure 4 This is a graph showing the change in detection probability as a function of signal-to-noise ratio in an embodiment of the present invention.

[0027] Figure 5 The graphs shown are the detection probability RMSE and average running time as a function of the number of Monte Carlo iterations in the embodiments of the present invention. (a) is the graph showing the RMSE of the detection probability fitted by the Gamma distribution of the present invention relative to the statistically calculated detection probability as a function of the number of Monte Carlo iterations, and (b) is the graph showing the average running time as a function of the number of Monte Carlo iterations based on the detection probability fitted by the Gamma distribution of the present invention and the statistically calculated detection probability. Detailed Implementation

[0028] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0029] Specific Implementation Plan 1: Combining Figure 1 As shown, this invention provides a method for analyzing the detection probability of a CA-CFAR detector under exponentially distributed noise background, comprising the following steps:

[0030] S100. Using the Gamma distribution to determine the detection statistic under target presence conditions. The probability distribution is fitted; the real part of the signal plus noise in the unit under test under the condition that the target exists. , follows the mean Standard deviation is Gaussian distribution, imaginary part Follow the mean Standard deviation is The Gaussian distribution, where the probability density functions of the real and imaginary parts of the signal plus noise in the unit under test under the condition of the target presence are denoted as follows: and ,in, The independent variable represents the probability density function;

[0031] Depend on and Calculate the detection statistic given the presence of the target. mean and variance Then, the shape parameters of the Gamma distribution under this mean and variance are calculated. and scale parameters Therefore, the detection statistic can be obtained under the condition that the target exists. probability density function ;

[0032] in, , , The expression is as follows:

[0033] (5)

[0034] (6)

[0035] (7)

[0036] In the formula, ; It is the Gamma function; For without coefficient and The product of the two, with coefficients set to ; The ratio of the instantaneous echo power to the average noise power in the unit under test is given by the relationship between the signal-to-noise ratio (SNR) and the signal-to-noise ratio (SNR). ;

[0037] S200, Given the signal-to-noise ratio (SNR) and reference cell length... The probability density function for noise power level estimation The probability density function of the detection statistic under the condition that the target exists. and standardization factor In this case, the detection probability can be calculated, and this detection probability is called the Gamma distribution fitted detection probability, denoted as . ; The expression is as follows:

[0038] (8)

[0039] In the formula, It is a generalized hypergeometric function. , , , It is the independent variable of the function. for exist Take 2, A special case when taking 1, Also known as hypergeometric functions.

[0040] Specific implementation scheme 2: The present invention provides a CA-CFAR detector detection probability analysis system under noisy background. The system has a program module corresponding to the above steps, and executes the steps in the above-mentioned CA-CFAR detector detection probability analysis method under noisy background when running.

[0041] The other combinations and connections in this implementation scheme are the same as in Specific Implementation Scheme 1.

[0042] Specific Implementation Scheme 3: The present invention provides a computer-readable storage medium storing a computer program configured to implement, when called by a processor, the steps of a method for analyzing the detection probability of a CA-CFAR detector under noisy background.

[0043] The other combinations and connections in this implementation scheme are the same as in Specific Implementation Scheme 1.

[0044] Simulation Experiment

[0045] To verify the accuracy of the detection probability calculation model proposed in this invention, simulation experiments were conducted. The data used here is simulation data based on the actual active sonar system's functional and performance parameters and typical operating environment: This experiment simulates the noise component mixed in the echo signal received by the active sonar, which is received by a hydrophone and converted into a voltage signal. This signal is then processed by hardware such as a preamplifier, bandpass filter, and analog-to-digital converter to finally obtain digitized noise. By performing square-law detection on this signal, the instantaneous power of the noise can be obtained, and its statistical characteristics follow an exponential distribution model. This simulation is based on the noise data generated by this physical process to conduct subsequent calculations and comparative analyses of the detection probability.

[0046] The simulation conditions are as follows: signal-to-noise ratio (SNR) is sampled at 1dB intervals from -30dB to 15dB, and the exponential distribution scaling parameter is used. The value is 1, which represents the length of the protection unit of the CA-CFAR detector. Value 50, reference unit length Take 15 points evenly from 1 to 50 (round to the nearest integer), and use the normalization factor. Take 15 points evenly from 0 to 0.05, and calculate the Monte Carlo degree. 15 points (rounded to integers) are selected logarithmically from 1 to 1000. The signal is an HFM signal with a center frequency of 100kHz, a bandwidth of 10kHz, a pulse width of 300ms, and a sampling rate of 100KHz.

[0047] for , For each combination of SNR, calculate using equation (8). ,for , , For each combination of SNR, the Monte Carlo method was used to calculate... The specific process of calculating the detection probability in a Monte Carlo experiment is as follows: the noise is divided into... The process involves generating the target echo signal according to pre-set signal parameters, performing matched filtering, and then normalizing the filtered signal. The noise power is then calculated. The signal amplitude required to satisfy the signal-to-noise ratio (SNR) , will satisfy the amplitude The matched filter output signal is superimposed with noise, and the squared modulus is used as the detection statistic for CA-CFAR signal detection. The number of times the signal is detected is related to... The ratio is the detection probability.

[0048] Drawing reference cell length When the signal-to-noise ratio (SNR) is 50, the statistical calculation results of the probability density function of the detection statistic and the fitting of the Gamma distribution under the condition of target presence when the SNR is -10dB and 10dB are as follows: Figure 2 As shown. By Figure 2 It can be seen that the probability density function of the detection statistic can be fitted by the Gamma distribution when the target exists.

[0049] Drawing reference cell length When the value is 50, the detection probability is fitted by the Gamma distribution. and statistical calculation of detection probability With signal-to-noise ratio (SNR) and nominalization factor Changing pseudo-color images, such as Figure 3 As shown. The length of the reference cell is plotted. Take 50, standardization factor When the value is 0.05, the detection probability is fitted by the Gamma distribution. and statistical calculation of detection probability The curve of SNR variation with signal-to-noise ratio is as follows Figure 4 As shown. By Figure 3 and Figure 4 It can be seen that, in the same , conditions, and It exhibits good consistency. This further demonstrates that the detection probability calculation model based on Gamma distribution fitting has high accuracy.

[0050] Based on this, the root mean square error (RMSE) and average computation time are used to quantitatively calculate the model accuracy and computational efficiency, respectively. , … Under the parameter combination, a certain parameter Values At that time, the RMSE of Model 1 relative to Model 2 and the average computation time of Model 1 were... Calculate according to equations (9) and (10) respectively.

[0051] (9)

[0052] (10)

[0053] In the formula, For all parameter combinations Pick The number of combinations, , and They are respectively Pick The first combination The calculation results of Model 1, the calculation results of Model 2, and the calculation time of Model 1 for each combination.

[0054] Calculate different using equation (9) Values Model relative to The RMSE is calculated using equation (10). and Average computation time, calculation results Figure 5 As shown.

[0055] Due to the present invention The model is independent of the Monte Carlo degree, and the calculation results do not change with the Monte Carlo degree. Figure 5 (a) shows that as the Monte Carlo number increases, Model relative to The RMSE first decreased and then tended to stabilize, indicating that The model approximates the Monte Carlo method as the Monte Carlo value increases. Model calculation results. According to Monte Carlo simulation theory, as the Monte Carlo degree increases, It converges to the true detection probability. Therefore, this indicates... The model's calculation results are close to the true false alarm probability.

[0056] Further analysis based on the above conclusions Figure 5 The reason for the trend of RMSE change in (a) is that when the Monte Carlo number is small, The statistical error relative to the true detection probability is greater than The inherent error of the model's calculation results relative to the true detection probability increases with the Monte Carlo iteration. The inherent error of the model remains unchanged. The statistical error is reduced, thus leading to Compared to The RMSE decreases as the Monte Carlo number increases. When it is close enough to the true detection probability Compared to The RMSE is The inherent error, therefore Compared to The RMSE tends to stabilize. Figure 5 In (a), when the Monte Carlo degree is 1000... Model relative to The RMSE tends to stabilize. This indicates that when the number of Monte Carlo simulations is less than 1000, The model's inherent error is always less than The systematic error. (By) Figure 5 (b) It can be seen that, The average running time of the model for 236 Monte Carlo experiments achieves the accuracy of calculations from 1000 Monte Carlo experiments. This demonstrates the effectiveness of the method proposed in this invention. The model maintains high accuracy on simulation data while exhibiting significantly better computational efficiency than the Monte Carlo method.

[0057] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A method for analyzing the detection probability of a CA-CFAR detector under noisy conditions, characterized in that, Includes the following steps: S100. Fit the probability distribution of the detection statistic under the condition of target presence using the Gamma distribution, including calculating the real and imaginary probability density functions of the signal plus noise in the unit under test under the condition of target presence, then calculating the mean and variance of the detection statistic under the condition of target presence, and then calculating the shape parameter and scale parameter of the Gamma distribution under the mean and variance to obtain the probability density function of the detection statistic under the condition of target presence. S200. Given the signal-to-noise ratio, reference cell length, probability density function of noise power level estimation, probability density function of detection statistic under target presence condition, and standardization factor, the detection probability is calculated.

2. The method for analyzing the detection probability of a CA-CFAR detector under noisy background according to claim 1, characterized in that: In step S100, the detection statistic is determined under the condition that the target exists. probability density function Shape parameters of the Gamma distribution Scale parameters of the Gamma distribution The expression is as follows: (1) (2) (3) In the formula, ; It is the Gamma function; For without coefficient and The product of the two, with coefficients set to ; The ratio of the instantaneous echo power to the average noise power in the unit under test is given by the relationship between the signal-to-noise ratio (SNR) and the signal-to-noise ratio (SNR). .

3. The method for analyzing the detection probability of a CA-CFAR detector under noisy background according to claim 2, characterized in that: Detecting probability in step S200 The expression is as follows: (4) In the formula, It is a generalized hypergeometric function. , , , It is the independent variable of the function. for exist Take 2, A special case when taking 1, Also known as hypergeometric functions.

4. A detection probability analysis system for a CA-CFAR detector under noisy background, characterized in that: The system has a program module corresponding to the steps of any one of the claims 1-3 above, and executes the steps in the above-described method for analyzing the detection probability of a CA-CFAR detector under noisy background when it is run.

5. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program configured to, when invoked by a processor, implement the steps of the CA-CFAR detector detection probability analysis method under noisy background as described in any one of claims 1-3.

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